Computed tomography (CT) systems and methods are widely used, particularly for medical imaging and diagnosis. A CT scan can be performed by positioning a patient on a CT scanner in a space between an X-ray source and X-ray detector, and then taking X-ray projection images through the patient at different angles as the X-ray source and detector are rotated through a scan. The resulting projection data is referred to as a CT sinogram, which represents attenuation through the body as a function of position along one or more axis and as a function of projection angle along another axis. Performing an inverse Radon transform—or any other image reconstruction method—on the projection data to reconstruct a tomographic image.
Various methods can be used to reconstruct CT images from projection data, including filtered back-projection (FBP) and statistical iterative reconstruction (IR) algorithms. Compared to FBP reconstruction methods, IR methods can provide improved image quality at reduced radiation doses. Often IR methods include a regularization term (also referred to as a “regularizer”) to encourage/constrain/impose a particular aspect or quality in the reconstructed image (e.g., smoothness or piecewise uniformity in the radiodensity). For example, when the regularizer imposes smoothness on the reconstructed image, a regularization parameter β determines the degree of smoothing imposed, and the regularization parameter β can be spatially-varying to impose different degrees of smoothing at different points within the reconstructed image.
In J. A. Fessler et al., “Spatial Resolution Properties of Penalized-Likelihood Image Reconstruction: Space-Invariant Tomographs,” IEEE Transactions on Image Processing, vol. 5, 1346-1358 (1996) and in U.S. Pat. No. 9,478,049, a spatially-varying regularization parameter β was proposed to provide either uniform resolution or uniform statistical properties (e.g., signal-to-noise ration SNR) throughout a reconstructed image. However, sometimes images with uniform resolution or with uniform statistical properties do not produce an image with the best qualities for a particular application. Accordingly, improved methods are desired for reconstructing images for particular applications.